The present study addresses the problem of stress redistribution and instability in rotating orthotropic thick-walled cylinders. In the classical approach of determining the stresses and displacements due to a centrifugal force, the inertia force considered does not include the radial displacement. Inclusion of the radial displacement in the centrifugal force results in stress redistribution, and instability occurs at certain rotational speeds. Following a brief outline of the classical analysis, the stress redistribution solutions are presented. The solutions are obtained in terms of non-dimensional parameters. Various cases are considered and the corresponding radial displacement and stress distributions along with their comparisons with the classical results are presented graphically. Critical rotational parameters at the onset of instability are presented in tabular form. It has been shown that increasing the ratio of circumferential stiffness to radial stiffness increases the stability of the cylinder.